Variational Autoencoders (VAEs) [1]} have been shown to produce semantically meaningful and interpretable dimensional reductions into their latent space in many contexts. To be trained, they require a notion of similarity between pairs of objects to be used in the reconstruction loss. Pixel intensity based losses have been used in various VAE studies for collider data [2]}, [3]}, [4]}, but these fail to properly reflect the similarity of events with collinear splittings or small displacements. Given its appealing physical properties, the EMD between events is a promising candidate be used as the reconstruction loss in a VAE. This paper serves to introduce a VAE trained with such a reconstruction loss, and to describe some preliminary experiments and an investigation into their scaling behaviour, with the objective to understand what can be gleaned about the underlying dataset from studying the properties of the learnt representation. Instead of training on full LHC events, this study is restricted to individual \(W\) -jets, which are collimated streams of particles formed from the decay of a \(W\)  boson travelling with high momentum.
